Forecast It 2. Linear Regression & Model Statistics

8/9/2019 Forecast It 2. Linear Regression & Model Statistics

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Linear Regression and Model Statistics

Lesson #2

Linear Regression Method

Copyright 2010 DeepThought, Inc. 1


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Method Introduction One of the simpler methods to use for forecasting

Estimates a line through the data

Uses the estimated line equation to forecast future values.

Method Format:

Y = a + b * t



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Model Characteristics Method Characteristics

Fits a line to the data

Estimating a line which minimizes the errors between actual

data points and model estimates

When to use Method

Estimate trend

Estimate trend magnitude

When not to use

Estimate anything beyond a simple linear relationship.



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Forecasting Steps1. Objective Setting

2. Method Selection

3. Model Evaluation

4. Find Best Models

5. Use Best Models



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Objective Setting Simpler is better

Linear Regression allows to test whether a line fitted to the data

works as a model. Objectives should take that principal under

consideration.

Example Objectives for M2 Money Stock (see next slide):

Test if M2 has a linear trend over time.

If M2 exhibits a statistically significant trend , what is its

magnitude and does it make sense? If model looks good, Create a forecast based off model.



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Example: M2 Money Stock

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May-79 Nov-84 May-90 Oct-95 Apr-01 Oct-06 Apr-12

M2 Money Stock (Billions of $'s)



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Method Selection Observe time series qualities: trend, seasonality, cyclicality, and

randomness.

Adjust time frame, units, periods to forecast as needed.

Determine if linear regression is a possible candidate based onmethod characteristics.

Determine if transforming the units will enable use of model.

8 Different Unit Transformation Techniques



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Build Model Software finds us the best fit line to the data: (Minimizing the Sum

of Squared Errors)

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Evaluate Model Descriptive Statistics

Mean

Variance & Standard Deviation

Accuracy / Error

SSE

RMSE

MAPE

R-Squared; Adjusted R-Squared

Statistical Significance

F-Test

P-Value F-Test



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Descriptive StatisticsMean

The average value of the data set.

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Variance & Standard Deviation The sum of squared deviations of the data from the mean.

Estimates the variation the data exhibits from the mean

Standard Deviation is the squared root of the variance

Used to measure the distribution of the variable away from the

mean, most observations of the variable will be within 3

standard deviations.



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M2 Example Mean

4214.38

Variance

3346475.10

SD (Standard Deviation)

1829.34

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Accuracy/ErrorSSE

Sum of Square Errors (SSE) Sums the Errors between the actual

values and model values

Measures the total error of the model

M2 Example:

SSE: 316778645.89

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RMSE

The square root of the sum of square error divided by the number

of observations. An averaged out total of errors based upon the number of

observations.

Simple way to compare models based on error.

M2 Example:

RMSE: 456.82



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MAPE

The average percentage error of the model.

Describes the average percentage of variation exhibited betweenactual and forecasted values.

M2 Example:

MAPE: 10.09%

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R-Squared & Adjusted R-Squared

A proportion between unexplained and explained errors.

Measures the percentage of variation captured by the model. Adjusted R-Squared incorporated the number of variables used and

sample size to adjust the R-Squared value.



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M2 Example R2

93.76%

Adjusted R2

93.76%

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Statistical SignificanceF-Test

A proportion between explained and unexplained errors of model. Used to test if model build is statistically significant from being

equal to zero.

The larger the F-test the better.



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F-Test P-Value

The F-Test P-Valuerepresents the percentage of significance of the F-test. (Blue area on

graph)

The higher the value of the F-test the lower the shaded blue area is.

As the blue area decreases, confidence about our model being

statistically significant increases.

1 p-value = Significance Level of the Model (%)

Significance Level of the Model (%) represents the amount of

confidence we have that our model is different from a model with

no impact, or zero impact.Copyright 2010 DeepThought, Inc. 19


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M2 Example

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M2 Money Stock (Billions of $'s) F-Test

22778.98

F-Test P-Value

0.00



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Compare Multiple Models Skip this step until have knowledge of multiple methods.

Will use Accuracy/Error statistics to compare multiple models to

find best models



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Use Model Understand Limitations of Model.

Only measures a trend.

A long term average.

Answer Objectives.

Does M2 has a linear trend.

If trend exists, what is its magnitude.

If model statistically significant, forecast.



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M2 Example M2 = 1145.31 + 4.04 * Time

Next Period is 1519

Forecast for that period is:

Y = 1145.31 + 4.04 * 1519

Y = 7283.446866


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Forecast It 2. Linear Regression & Model Statistics

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